Deck 1: Equations and Inequalities

Question 1

Suppose a lunch consisting of a large hamburger, large fries and large soft drink at a fast food chain contains 1380 calories.A lunch consisting of a small hamburger, small fries and a small soft drink at the same fast food chain contains 880 calories.Find the percent change in calories from the smaller to the larger lunch.Round to the nearest hundredth of a percent.

A) 56.82% increase
B) 63.77% decrease
C) 63.77% increase
D) 36.23% increase
E) 56.82% decrease

Answer 1

A

Question 2

Find two consecutive integers whose product is 10 more than the square of the smaller number.

A)
B)
C)
D)
E)

Answer 2

C

Question 3

Solve the following equation.

A)
B)
C)
D)
E)

Answer 3

C

Question 4

Determine which of the following values of x is a solution to the equation

A)
B)
C)
D)
E)

Question 5

Solve:

A)
B)
C)
D)
E)

Question 6

Determine which of the following values of x is a solution to the equation

A)
B)
C)
D)
E)

Question 7

Solve the equation below.

A)
B)
C)
D)
E)

Question 8

Solve:

A)
B)
C)
D)
E)

Question 9

Translate the following statement into an algebraic expression.

A)
B)
C)
D)
E)

Question 10

The sum of two consecutive numbers is Which of the following equations describes this situation?

A)
B)
C)
D)
E)

Question 11

The length of a rectangle is 10 feet less than 4 times the width of a rectangle. If the perimeter of the rectangle is feet, find the width and the length.

A)
B)
C)
D)
E)

Question 12

Solve:

A)
B)
C)
D)
E)

Question 13

Solve the following equation.

A)
B)
C)
D)
E) 2

Question 14

Which of the following equations is not a conditional equation?

A)
B)
C)
D)
E)

Question 15

Solve the equation below.

A) -5
B) -2
C) -4
D) 8
E) 10

Question 16

The relationship between the length of an adult's femur (thigh bone) and the height of the adult can be approximated by the linear equations Female Male where is the length of the femur in inches and x is the height of the adult in inches (see figure). An anthropologist discovers a femur belonging to an adult human female.The bone is 12 inches long.Estimate the height of the female.Round to the nearest tenth of an inch.

A) 50.1 inches
B) 48.9 inches
C) 51.9 inches
D) 50.7 inches
E) 55.0 inches

Question 17

Which of the following equations is not an identity equation?

A)
B)
C)
D)
E)

Question 18

Solve for x, rounding your answer to the nearest thousandth.

A) -0.548
B) 1.059
C) -0.281
D) -0.478
E) -0.127

Question 19

You accept a new job with a starting salary of $56,000.You receive a 4.9% raise at the start of your second year, a 7.4% raise at the start of your third year, and a 8% raise at the start of your fourth year.Find your salary for the fourth year.

A) $68,138.34
B) $66,854.44
C) $67,881.56
D) $68,651.90
E) $69,422.24

Question 20

Your weekly paycheck is 16% more than your coworker's.Your two paychecks total $1188.Find the amount of your coworker's paycheck.

A) $587
B) $638
C) $502
D) $694
E) $550

Question 21

Solve by factoring.

A)
B)
C)
D)
E)

Question 22

Solve the quadratic equation below by factoring.

A)
B)
C)
D)
E)

Question 23

Solve the quadratic equation by any convenient method.

A) and
B) and
C) and
D) and
E) and

Question 24

Assume that air resistance is negligible, which implies that the position equation is a reasonable model.A rock is dropped from the top of a 140-foot cliff that overlooks the ocean.How long will it take for the rock to hit the water? Round to the nearest hundredth of a second.

A) 3.92 seconds
B) 2.96 seconds
C) 7.78 seconds
D) 8.75 seconds
E) 6.82 seconds

Question 25

Write in general form.

A)
B)
C)
D)
E)

Question 26

Two friends fly from from one city to another (a distance apart of 2417 miles).It takes 2 hours and 25 minutes to fly the first 860 miles.At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

A) 8.15 hours
B) 6.79 hours
C) 6.34 hours
D) 5.89 hours
E) 7.24 hours

Question 27

How many liters of a 25% acid solution should be mixed with 3 liters of a 15% acid solution to produce a 23% solution?

A) 4 liters
B) 12 liters
C) 7 liters
D) 2 liters
E) 6 liters

Question 28

An investment adviser invested in two accounts. One investment earned 6% annual simple interest, and the other investment earned 7.5% annual simple interest. The amount of interest earned for 1 year was How much was invested in each account?

A) @ 6%; @ 7.5%
B) @ 6%; @ 7.5%
C) $50,000 @ 6%; $40,000 @ 7.5%
D) @ 6%; @ 7.5%
E) @ 6%; @ 7.5%

Question 29

To determine the height of a tree, you measure its shadow and the shadow of a five-foot lamppost.The shadow of the lamppost is 2 feet and the shadow of the tree is 25 feet.Assuming both the tree and the lamppost are standing next to each other and perpendicular to the ground, how tall is the tree? Round to the nearest tenth of a foot.

A) 62.5 feet
B) 36.3 feet
C) 80.0 feet
D) 10.0 feet
E) 18.8 feet

Question 30

The demand equation for a product is where is the price per unit and is the number of units sold.The total revenue for selling units is given by How many units must be sold to produce a revenue of $45,000?

A) 6000 units
B) 3000 units
C) 9000 units
D) 12,000 units
E) 15,000 units

Question 31

The price of a computer fell 15% this year.If the computer now costs $680, how much did it cost last year?

A) $760
B) $820
C) $800
D) $780
E) $790

Question 32

Solve:

A)
B)
C)
D)
E)

Question 33

Solve the quadratic equation below by extracting square roots.Round to two decimal places.

A)
B)
C)
D)
E)

Question 34

A rectangular pool is 40 feet wide and 45 feet long.It is surrounded on all four sides by a wooden deck of fixed width.The total area enclosed within the perimeter of the deck is 2354 square feet.What is the width of the deck?

A) 9 feet
B) 8 feet
C) 4 feet
D) 11 feet
E) 12 feet

Question 35

Solve by any convenient method.

A)
B)
C)
D)
E)

Question 36

Solve by extracting square roots.

A)
B)
C)
D)
E)

Question 37

How much water must be added to 8 liters of a 51% saline solution to dilute it to a 36% saline solution? Round answer to nearest tenth of a liter.

A) 3.1 liters
B) 3.3 liters
C) 3.5 liters
D) 3.7 liters
E) 3.9 liters

Question 38

Variable costs depend on the number of units produced.Fixed costs are the same regardless of how many units are produced.A company has fixed monthly costs of $17,000 and variable monthly costs of $6.00 per unit.The company has $95,000 available each month to cover costs.Find the greatest number of units the company can produce each month.

A) 13,000 units per month
B) 12,991 units per month
C) 12,987 units per month
D) 12,998 units per month
E) 13,014 units per month

Question 39

Use the discriminant to determine the number of real solutions of the quadratic equation below.

A) one real solutions
B) three real solutions
C) four real solutions
D) two real solutions
E) no real solutions

Question 40

The price of a home theater system has been discounted 18%.The sale price is $289.Find the original price of the system.

A) $341.02
B) $356.25
C) $363.86
D) $352.44
E) $348.63

Question 41

Determine the number of real solutions of by using the discriminant.

A) 2
B) 1
C) none

Question 42

One number is 1 more than another number.The sum of their squares is 41.Find the numbers.

A) 4, 5 or -5, -4
B) 3, 4 or -4, -3
C) 9, 10 or -10, -9
D) 2, 3 or -3, -2
E) 7, 8 or -8, -7

Question 43

A square piece of cardboard is formed into a box by cutting out 3-inch squares from each of the corners and folding up the sides.If the volume of the box needs to be 90.75 cubic inches, what size square piece of cardboard is needed?

A) 10.0 inches by 10.0 inches
B) 14.0 inches by 14.0 inches
C) 2.5 inches by 2.5 inches
D) 8.5 inches by 8.5 inches
E) 11.5 inches by 11.5 inches

Question 44

Solve the following polynomial equation by factoring and using the zero factor property.

A)
B)
C)
D)
E)

Question 45

Solve using the quadratic formula.

A)
B)
C)
D)
E)

Question 46

The demand equation for a product is where is the price per unit and is the number of units sold.The total revenue for selling units is given by How many units must be sold to produce a revenue of $220,000?

A) 96,188 units or 155,825 units
B) 3541 units or 103,541 units
C) 3541 units or 155,825 units
D) 3812 units or 96,188 units
E) 3541 units or 3812 units

Question 47

Use the cost equation to find the number of units x that a manufacturer can produce when Round answer to the nearest whole unit.

A) 365 units
B) 357 units
C) 344 units
D) 336 units
E) 330 units

Question 48

Find the real solutions of the radical equation.

A) -100
B) -10
C) 120
D) -20
E) 50

Question 49

Solve using the quadratic formula.Round answers to nearest thousandth.

A)
B)
C)
D)
E)

Question 50

Find the real solutions of the polynomial equation.

A)
B)
C)
D)
E)

Question 51

Find the real solutions of the radical equation.

A) 7
B) 4
C) 49
D) -9
E) -3

Question 52

Two planes leave simultaneously from the same airport, one flying due east and the other due south.The eastbound plane is flying 75 miles per hour slower than the southbound plane.After 3 hours the planes are 1863 miles apart.Find the speed of the southbound plane.

A) 475 miles per hour
B) 350 miles per hour
C) 375 miles per hour
D) 425 miles per hour
E) 400 miles per hour

Question 53

Solve the quadratic equation below using any convenient method.

A)
B)
C)
D)
E)

Question 54

A veterinarian wishes to use 84 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown below.If the total enclosed area is 270 square feet, find the dimensions of the enclosed area.

A) or
B) or
C) or
D) or
E) or

Question 55

Find the real solutions of the polynomial equation below.

A)
B)
C)
D)
E)

Question 56

Find the real solutions of the polynomial equation below.

A)
B)
C)
D)
E)

Question 57

Use the Quadratic Formula to solve the quadratic equation below.

A)
B)
C)
D)
E)

Question 58

A windlass is used to tow a boat to a dock.The figure shows a situation in which there are feet of rope extended to the boat feet away from the dock.How far is the boat from the dock if feet and feet? Round to the nearest tenth of a foot.

A) 26.0 feet
B) 7.6 feet
C) 62.8 feet
D) 16.8 feet
E) 44.4 feet

Question 59

Use the quadratic formula to solve the equation.

A)
B)
C)
D)
E)

Question 60

The height, h, in feet, of a baseball above the ground t seconds after it is hit is given by Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

A) 2.7 s
B) 2.8 s
C) 2.9 s
D) 3.0 s
E) 3.1 s

Question 61

Find all solutions of

A)
B)
C)
D)
E)

Question 62

A college charters a bus for $1848 to take a group of students to the Fiesta Bowl.When two more students join the trip, the cost per student decreases by $2.00.How many students were in the original group?

A) 42
B) 28
C) 34
D) 41
E) 49

Question 63

Find the real solutions of the equation below involving absolute value.Check your solutions.

A)
B)
C)
D)
E)

Question 64

Find all solutions of

A)
B)
C)
D)
E)

Question 65

Find all solutions of

A)
B)
C)
D)
E)

Question 66

The SMOG (Simplified Measure of Gobbledygook) readability formula estimates the reading grade level required by a person if he or she is to fully understand the written material assessed.The SMOG formula is defined as SMOG reading grade level where w is the number of words that have three or more syllables that should appear in a sample of 30 sentences.A writer of children's books has decided to write a book that can be fully understood by children at the 7th-grade level.What is the maximum number of words with three or more syllables that should appear in any sample of 30 sentences of the book?

A) 18
B) 20
C) 16
D) 17
E) 19

Question 67

Solve the rational equation below.

A) -8
B) -19
C) -17
D) 6
E) -4

Question 68

Match the inequality with its graph.

A)
B)
C)
D)
E)

Question 69

Use interval notation to express the solution set for the inequality below.

A)
B)
C)
D)
E)

Question 70

Write an inequality that represents the interval

A)
B)
C)
D)
E)

Question 71

Solve:

A)
B)
C)
D)
E) no solution

Question 72

The number of new privately-owned housing projects (in thousands) started from 2000 to 2005 can be modeled by where represents the year, with corresponding to 2000.Use the model to predict the year that about 1,600,000 new housing projects were started.

A) 2002
B) 2001
C) 2000
D) 2003
E) 2004

Question 73

Match the inequality with its graph.

A)
B)
C)
D)
E)

Question 74

Solve the following absolute value equation for

A) 1
B) 3
C) -3, 3
D) -13, 1
E) -13, 3

Question 75

Match the inequality with its graph.

A)
B)
C)
D)
E)

Question 76

Solve the inequality below.

A)
B)
C)
D)
E)

Question 77

Use interval notation to express the solution set of the inequality below.

A)
B)
C)
D)
E)

Question 78

A professional painter can paint a kitchen in 9 hours.His apprentice can paint the same kitchen in 12 hours. If they worked together, how long would it take for them to paint the kitchen?

A) 11
B)
C)
D) 3
E)

Question 79

Which of the following is not a solution to the inequality ?

A)
B)
C)
D)
E)

Question 80

Which of the following is not a solution to the inequality ?

A)
B)
C)
D)
E)